EDITED Resources. The resources on this page have been aligned with the revised K-12 mathematics TEKS. Necessary updates to the resources are in progress and will be completed Fall 2006. These revised TEKS were adopted by the Texas State Board of Education in 2005–06, with full implementation scheduled for 2006–07.

Clarifying Lessons

Grade 6: And Around We Go!

activity under revision

Lesson Overview

Students conduct a survey and collect data to construct a bar graph that will then be changed into a circle graph. With the bar graph, students will compare estimated fractions and percentages and will estimate percentages. With the circle graph, students will estimate fraction and percentage benchmark values.

Mathematics Overview

Students conduct a survey to collect, organize, display, and interpret data. Students will also use models to develop estimation strategies with fractions and percentages.

Set-up (to set the stage and motivate the students to participate)

Students survey the whole class and fill in the interest inventory on their favorite sport, soft drink, music, and color.

Tip: The total number of people polled will ideally be a number that is not easy to estimate the percentage of, such as 17 or 21. Also, the group number should ideally be under 25 so that the graphs will fit on the grid paper.

Activity 1:

  1. Assign one of the interest inventory questions to each small group of students. Instruct groups to sort the data and construct a bar graph using the Activity 1 worksheet. Advise each group to use markers to color each bar a different color.
  2. Once each group's bar graph is completed, have the students record the fractional part of the data represented by each bar of the graph and transfer graphs to large grid paper.
  3. Display each group's bar graphs and discuss conclusions that can be drawn from the graphs.
  4. Discuss other ways of displaying the data.

Activity 2:

  1. Ask students to use the remaining graph paper to create strips, following the directions on the Activity 2 worksheet. Each strip should be cut to the length of the number of people surveyed. For example, if nineteen people are surveyed, the strips should be nineteen inches long. Note that part of the bar will be colored, and part will not. Then each bar should be split vertically into one-inch strips.
  2. Using one set of these strips, students can determine benchmark fractions and percentages to describe their data. Using a folding method, students fold the strip in half. The teacher asks, "Is the shaded region greater or less than half? If it is less than one half, how much less? If it is greater, how much greater? Can you fold the strip again to get a better estimate of the fractional part?" Use the process of folding the strips in halves, fourths, thirds, etc. to determine the fractional part. If the whole bar represents 100% then estimate the percentage of the strip that is shaded.

Activity 3:

  1. Students complete the Activity 3 worksheet. The teacher may need to model the procedure with the students.
  2. Display the circle graphs next to the bar graphs saved from the first activity. Discuss what each representation shows.

Teacher Notes (to personalize the lesson for your classroom)

Guiding Questions (to engage students in mathematical thinking during the lesson)

  • What did you notice about the data you collected?
  • What data had the most responses? The least? Were any about the same?
  • How did you find the fractional part of data represented by each bar of the graph?
  • What is the "whole" of the fractional part and what does it represent?
  • Are any of your bars close to 1/2 of the whole set of data? Close to 1/3 of the data? Close to 1/4 of the data? How did you determine this?
  • Are the actual fractional parts "nice" fractions?
  • What strategy did you use to determine whether your estimate is greater than or less than the actual fractions?
  • How did you determine the estimated percentage of each bar?
  • Does the estimated percentage seem to match your estimated fractional part?
  • Do your estimated percentages add to be 100%? Why or why not?
  • What measurement can you estimate from the circle you created?
  • How did you estimate the diameter of the circle?
  • How did you determine the different sections of the circle graph?
  • How did you label each section of the circle graph?
  • How do your estimates of the sections of the circle graph compare to the estimates of fractional parts? Percentages?
  • What does the bar graph tell you that the circle graph does not?
  • What does the circle graph tell you that the bar graph does not?

Teacher Notes (to personalize the lesson for your classroom)

Summary Questions (to direct students' attention to the key mathematics in the lesson)

  • What strategy can you use to estimate fractions? Percentages?
  • Is it easier for you to estimate fractions or percentages? Why?
  • Once you have estimated fractional parts can you change this estimate to an estimated percentage?
  • Which display of data did you find most useful? Why?
  • How can you compare your estimate of the fractional size to the actual fractional part?
  • Did your fractional parts equal 1? Why or why not?
  • How do you display categories that have zero responses in a bar graph? Circle graph?
  • In your circle graph, does the circle have to have the same circumference as your model?
  • Can you create a circle graph directly from data collected?
  • What strategy would you use to estimate the sections the circle graph is divided into?
  • What information can you get from the bar graph that you cannot get from the circle graph?
  • What information can you get from the circle graph that you cannot get from the bar graph?

Teacher Notes (to personalize the lesson for your classroom)

Assessment Task(s) (to identify the mathematics students have learned in the lesson)

Collect additional data of interest. Have students organize, graph, and analyze the data. Have students estimate the percentages of each set of data and compare to the fractional parts.

Teacher Notes (to personalize the lesson for your classroom)

Extension(s) (to lead students to connect the mathematics learned to other situations, both within and outside the classroom)

  • Construct an "exact" circle graph with the data, using the fractional values and proportionality to determine the angle measures.
  • Use the TI-73 or similar calculator to create a circle graph.

Teacher Notes (to personalize the lesson for your classroom)